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On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics

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Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain a formula for the expansion of an arbitrary function in a series in the eigenfunctions of the Sturm–Liouville boundary-value problem for the differential equation of cone functions. On the basis of this result, we derive a series of integral transformations (including well-known ones) and inversion formulas for them. We apply these formulas to the solution of initial boundary-value problems in the theory of heat conduction for circular hollow cones truncated by spherical surfaces.

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Authors and Affiliations

  1. Institute of Mathematics, Economics, and Mechanics, Odessa University, Odessa

    G. Ya. Popov

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  1. G. Ya. Popov
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Popov, G.Y. On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics. Ukrainian Mathematical Journal 53, 951–964 (2001). https://doi.org/10.1023/A:1013304002593

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  • DOI: https://doi.org/10.1023/A:1013304002593

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